Question

Which $n$ satisfy $4xyz=n(x+y+z)$?

score 110 · Answer 1 · 2023-08-08 05:20:41

110

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Which $n$ satisfy $4xyz=n(x+y+z)$?

Published on 08 Aug 2023 - 5:20

score 131 · Answer 2 · 2026-03-25 12:53:34

131

Views

Finding or parametrizing integer solutions to $pq(p^2-q^2)=rs(r^2-s^2)$

Published on 25 Mar 2026 - 12:53

score 72 · Answer 3 · 2026-03-25 08:01:49

72

Views

Do $p_n$ minus the number of integer solutions to this equation equal $(-1)^{\frac{1}{24} \left((p_n){}^2-1\right)}$ for $n>4$?

Published on 25 Mar 2026 - 8:01

score 68 · Answer 4 · 2023-08-10 16:01:43

68

Views

Solving the Diophantine Equation $Axy^2 + Bxz^2 + Cy + Dz = 0$

Published on 10 Aug 2023 - 16:01

score 62 · Answer 5 · 2026-04-02 03:36:37

62

Views

Relation between Diophantine equations involving multiple sums with the modulo function and greatest common divisor function.

Published on 02 Apr 2026 - 3:36

score 173 · Answer 6 · 2023-08-12 07:30:13

173

Views

find all rational numbers $x,y$ such that we have : $x^3+y^3=x^2+y^2$

Published on 12 Aug 2023 - 7:30

score 148 · Answer 7 · 2026-03-25 22:04:16

148

Views

For which $x,n$ is the finite geometric series a perfect power?

Published on 25 Mar 2026 - 22:04

score 210 · Answer 8 · 2026-03-29 21:54:06

210

Views

On Sixth Powers $x_1^6+x_2^6+x_3^6+\dots+x_7^6 = z^6$ revisited

Published on 29 Mar 2026 - 21:54

score 228 · Answer 9 · 2023-08-15 10:26:15

228

Views

find all $m,n\in\mathbb{N}$ so that $\large\frac{n^3+1}{mn-1}$ $\in$ $\mathbb{N}$

Published on 15 Aug 2023 - 10:26

score 64 · Answer 10 · 2026-03-27 20:01:07

64

Views

Squares and geometric series

Published on 27 Mar 2026 - 20:01

score 75 · Answer 11 · 2026-04-05 12:07:07

75

Views

Factoring using the Brahmagupta Identity

Published on 05 Apr 2026 - 12:07

score 553 · Answer 12 · 2026-03-29 21:57:03

553

Views

How did Scott Chase find the only solution to eighth powers $x_1^8 + x_2^8 + x_3^8 + x_4^8 + \dots + x_8^8 = 1409^8$ back in 2000?

Published on 29 Mar 2026 - 21:57

score 403 · Answer 13 · 2026-03-28 08:50:02

403

Views

How can you prove or disprove that half of all natural numbers can be expressed as the sum of three squares minus the product of their roots?

Published on 28 Mar 2026 - 8:50

score 63 · Answer 14 · 2023-08-26 11:40:47

63

Views

solve $10^k - 10^r = ax$ over the integers

Published on 26 Aug 2023 - 11:40

score 76 · Answer 15 · 2023-08-26 17:42:53

76

Views

Solving the diophantine equation $6x^2 + y^2 + 6x = 3xy + 6y + x^2y$

Published on 26 Aug 2023 - 17:42

List Question

Which $n$ satisfy $4xyz=n(x+y+z)$?

Finding or parametrizing integer solutions to $pq(p^2-q^2)=rs(r^2-s^2)$

Do $p_n$ minus the number of integer solutions to this equation equal $(-1)^{\frac{1}{24} \left((p_n){}^2-1\right)}$ for $n>4$?

Solving the Diophantine Equation $Axy^2 + Bxz^2 + Cy + Dz = 0$

Relation between Diophantine equations involving multiple sums with the modulo function and greatest common divisor function.

find all rational numbers $x,y$ such that we have : $x^3+y^3=x^2+y^2$

For which $x,n$ is the finite geometric series a perfect power?

On Sixth Powers $x_1^6+x_2^6+x_3^6+\dots+x_7^6 = z^6$ revisited

find all $m,n\in\mathbb{N}$ so that $\large\frac{n^3+1}{mn-1}$ $\in$ $\mathbb{N}$

Squares and geometric series

Factoring using the Brahmagupta Identity

How did Scott Chase find the only solution to eighth powers $x_1^8 + x_2^8 + x_3^8 + x_4^8 + \dots + x_8^8 = 1409^8$ back in 2000?

How can you prove or disprove that half of all natural numbers can be expressed as the sum of three squares minus the product of their roots?

solve $10^k - 10^r = ax$ over the integers

Solving the diophantine equation $6x^2 + y^2 + 6x = 3xy + 6y + x^2y$

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